RudyLopez
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☣☣☣☣☣☣☣Suppose you have 76 feet of fencing to enclose a rectangular dog pen. The function A=38x - x^2 where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary.☣☣☣☣☣☣

A.) width = 19 ft; area = 1083 ft2

B.) width = 19 ft; area = 361 ft2

C.) width = 38 ft; area = 361 ft2

D.) width = 38 ft; area = 760 ft2

Respuesta :

Answer:

Option B is correct

width = 19 ft; area = 361 [tex]ft^2[/tex]

Step-by-step explanation:

For a quadratic equation:

[tex]y=ax^2+bx+c[/tex]             .....[1]

the axis of symmetry is given by:

[tex]x = -\frac{b}{2a}[/tex]

As per the statement:

The function is given by:

[tex]A = 38x-x^2[/tex]          .....[2]

where,

x is the width of the rectangular dog pen.

On comparing the given equation with [1] we have;

a = -1  and b = 38

then;

[tex]x = -\frac{38}{2(-1)}[/tex]

⇒[tex]x = \frac{38}{2}[/tex]

Simplify:

x = 19 ft.

Substitute in [2] to find the maximum area:

[tex]A_{max} = 38(19)-19^2 = 722-361 = 361 ft^2[/tex]

Therefore, 19 ft width gives you the maximum area and the maximum area is, 361 square ft.

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